Symplectic embeddings and the Lagrangian bidisk

Abstract

In this article we obtain sharp obstructions to the symplectic embedding of the Lagrangian bidisk into four-dimensional balls, ellipsoids, and symplectic polydisks. We prove, in fact, that the interior of the Lagrangian bidisk is symplectomorphic to a concave toric domain by using ideas that come from billiards on a round disk. In particular, we answer a question of Ostrover. We also obtain sharp obstructions to some embeddings of ellipsoids into the Lagrangian bidisk.